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</head><body class="rustdoc trait"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">☰</button><a class="sidebar-logo" href="../../halo2_proofs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div>
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</a><h2 class="location"><a href="#">Field</a></h2><div class="sidebar-elems"><section><div class="block"><h3 class="sidebar-title"><a href="#required-methods">Required Methods</a></h3><ul><li><a href="#tymethod.double">double</a></li><li><a href="#tymethod.invert">invert</a></li><li><a href="#tymethod.one">one</a></li><li><a href="#tymethod.random">random</a></li><li><a href="#tymethod.sqrt">sqrt</a></li><li><a href="#tymethod.square">square</a></li><li><a href="#tymethod.zero">zero</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#provided-methods">Provided Methods</a></h3><ul><li><a href="#method.cube">cube</a></li><li><a href="#method.is_zero">is_zero</a></li><li><a href="#method.is_zero_vartime">is_zero_vartime</a></li><li><a href="#method.pow_vartime">pow_vartime</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#foreign-impls">Implementations on Foreign Types</a></h3><ul><li><a href="#impl-Field-for-Fp">Fp</a></li><li><a href="#impl-Field-for-Fq">Fq</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#implementors">Implementors</a></h3></div></section><h2 class="location"><a href="index.html">In halo2_proofs::arithmetic</a></h2><div id="sidebar-vars" data-name="Field" data-ty="trait" data-relpath=""></div><script defer src="sidebar-items.js"></script></div></nav><main><div class="width-limiter"><div class="sub-container"><a class="sub-logo-container" href="../../halo2_proofs/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><nav class="sub"><div class="theme-picker hidden"><button id="theme-picker" aria-label="Pick another theme!" aria-haspopup="menu" title="themes"><img width="22" height="22" alt="Pick another theme!" src="../../brush.svg"></button><div id="theme-choices" role="menu"></div></div><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><button type="button" id="help-button" title="help">?</button><a id="settings-menu" href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></form></nav></div><section id="main-content" class="content"><div class="main-heading">
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<h1 class="fqn"><span class="in-band">Trait <a href="../index.html">halo2_proofs</a>::<wbr><a href="index.html">arithmetic</a>::<wbr><a class="trait" href="#">Field</a><button id="copy-path" onclick="copy_path(this)" title="Copy item path to clipboard"><img src="../../clipboard.svg" width="19" height="18" alt="Copy item path"></button></span></h1><span class="out-of-band"><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><div class="docblock item-decl"><pre class="rust trait"><code>pub trait Field: 'static + <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Copy.html" title="trait core::marker::Copy">Copy</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/default/trait.Default.html" title="trait core::default::Default">Default</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Send.html" title="trait core::marker::Send">Send</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sync.html" title="trait core::marker::Sync">Sync</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html" title="trait core::fmt::Debug">Debug</a> + <a class="trait" href="https://docs.rs/subtle/2.4.1/subtle/trait.ConditionallySelectable.html" title="trait subtle::ConditionallySelectable">ConditionallySelectable</a> + <a class="trait" href="https://docs.rs/subtle/2.4.1/subtle/trait.ConstantTimeEq.html" title="trait subtle::ConstantTimeEq">ConstantTimeEq</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a><Self, Output = Self, Output = Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Sub.html" title="trait core::ops::arith::Sub">Sub</a><Self, Output = Self, Output = Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><Self, Output = Self, Output = Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Neg.html" title="trait core::ops::arith::Neg">Neg</a><Output = Self> + for<'a> <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self> + for<'a> <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self> + for<'a> <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Sub.html" title="trait core::ops::arith::Sub">Sub</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a><Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a><Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.SubAssign.html" title="trait core::ops::arith::SubAssign">SubAssign</a><Self> + for<'a> <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self> + for<'a> <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self> + for<'a> <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.SubAssign.html" title="trait core::ops::arith::SubAssign">SubAssign</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self> {
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fn <a href="#tymethod.random" class="fnname">random</a>(rng: impl <a class="trait" href="https://rust-random.github.io/rand/rand_core/trait.RngCore.html" title="trait rand_core::RngCore">RngCore</a>) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.zero" class="fnname">zero</a>() -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.one" class="fnname">one</a>() -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.square" class="fnname">square</a>(&self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.double" class="fnname">double</a>(&self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.invert" class="fnname">invert</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Self>;
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<span class="item-spacer"></span> fn <a href="#tymethod.sqrt" class="fnname">sqrt</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Self>;
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fn <a href="#method.is_zero" class="fnname">is_zero</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.Choice.html" title="struct subtle::Choice">Choice</a> { ... }
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<span class="item-spacer"></span> fn <a href="#method.is_zero_vartime" class="fnname">is_zero_vartime</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> { ... }
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<span class="item-spacer"></span> fn <a href="#method.cube" class="fnname">cube</a>(&self) -> Self { ... }
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<span class="item-spacer"></span> fn <a href="#method.pow_vartime" class="fnname">pow_vartime</a><S>(&self, exp: S) -> Self<br> <span class="where">where<br> S: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.AsRef.html" title="trait core::convert::AsRef">AsRef</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u64.html">u64</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">]</a>></span>,
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{ ... }
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}</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>This trait represents an element of a field.</p>
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</div></details><h2 id="required-methods" class="small-section-header">Required Methods<a href="#required-methods" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle" open><summary><div id="tymethod.random" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.random" class="fnname">random</a>(rng: impl <a class="trait" href="https://rust-random.github.io/rand/rand_core/trait.RngCore.html" title="trait rand_core::RngCore">RngCore</a>) -> Self</h4></div></summary><div class="docblock"><p>Returns an element chosen uniformly at random using a user-provided RNG.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.zero" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.zero" class="fnname">zero</a>() -> Self</h4></div></summary><div class="docblock"><p>Returns the zero element of the field, the additive identity.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.one" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.one" class="fnname">one</a>() -> Self</h4></div></summary><div class="docblock"><p>Returns the one element of the field, the multiplicative identity.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.square" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.square" class="fnname">square</a>(&self) -> Self</h4></div></summary><div class="docblock"><p>Squares this element.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.double" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.double" class="fnname">double</a>(&self) -> Self</h4></div></summary><div class="docblock"><p>Doubles this element.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.invert" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.invert" class="fnname">invert</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Self></h4></div></summary><div class="docblock"><p>Computes the multiplicative inverse of this element,
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failing if the element is zero.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.sqrt" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.sqrt" class="fnname">sqrt</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Self></h4></div></summary><div class="docblock"><p>Returns the square root of the field element, if it is
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quadratic residue.</p>
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</div></details></div><h2 id="provided-methods" class="small-section-header">Provided Methods<a href="#provided-methods" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle" open><summary><div id="method.is_zero" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#method.is_zero" class="fnname">is_zero</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.Choice.html" title="struct subtle::Choice">Choice</a></h4></div></summary><div class="docblock"><p>Returns true iff this element is zero.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="method.is_zero_vartime" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#method.is_zero_vartime" class="fnname">is_zero_vartime</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></h4></div></summary><div class="docblock"><p>Returns true iff this element is zero.</p>
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<h5 id="security"><a href="#security">Security</a></h5>
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<p>This method provides <strong>no</strong> constant-time guarantees. Implementors of the
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<code>Field</code> trait <strong>may</strong> optimise this method using non-constant-time logic.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="method.cube" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#method.cube" class="fnname">cube</a>(&self) -> Self</h4></div></summary><div class="docblock"><p>Cubes this element.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="method.pow_vartime" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#method.pow_vartime" class="fnname">pow_vartime</a><S>(&self, exp: S) -> Self <span class="where fmt-newline">where<br> S: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.AsRef.html" title="trait core::convert::AsRef">AsRef</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u64.html">u64</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">]</a>>, </span></h4></div></summary><div class="docblock"><p>Exponentiates <code>self</code> by <code>exp</code>, where <code>exp</code> is a little-endian order
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integer exponent.</p>
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<p><strong>This operation is variable time with respect to the exponent.</strong> If the
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exponent is fixed, this operation is effectively constant time.</p>
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</div></details></div><h2 id="foreign-impls" class="small-section-header">Implementations on Foreign Types<a href="#foreign-impls" class="anchor"></a></h2><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Field-for-Fp" class="impl has-srclink"><a href="#impl-Field-for-Fp" class="anchor"></a><h3 class="code-header in-band">impl <a class="trait" href="trait.Field.html" title="trait halo2_proofs::arithmetic::Field">Field</a> for Fp</h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.sqrt" class="method trait-impl has-srclink"><a href="#method.sqrt" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.sqrt" class="fnname">sqrt</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Fp></h4></section></summary><div class="docblock"><p>Computes the square root of this element, if it exists.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.invert" class="method trait-impl has-srclink"><a href="#method.invert" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.invert" class="fnname">invert</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Fp></h4></section></summary><div class="docblock"><p>Computes the multiplicative inverse of this element,
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failing if the element is zero.</p>
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</div></details><section id="method.random" class="method trait-impl has-srclink"><a href="#method.random" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.random" class="fnname">random</a>(rng: impl <a class="trait" href="https://rust-random.github.io/rand/rand_core/trait.RngCore.html" title="trait rand_core::RngCore">RngCore</a>) -> Fp</h4></section><section id="method.zero" class="method trait-impl has-srclink"><a href="#method.zero" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.zero" class="fnname">zero</a>() -> Fp</h4></section><section id="method.one" class="method trait-impl has-srclink"><a href="#method.one" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.one" class="fnname">one</a>() -> Fp</h4></section><section id="method.double" class="method trait-impl has-srclink"><a href="#method.double" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.double" class="fnname">double</a>(&self) -> Fp</h4></section><section id="method.square" class="method trait-impl has-srclink"><a href="#method.square" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.square" class="fnname">square</a>(&self) -> Fp</h4></section><section id="method.pow_vartime-1" class="method trait-impl has-srclink"><a href="#method.pow_vartime-1" class="anchor"></a><h4 class="code-header">fn <a href="#method.pow_vartime" class="fnname">pow_vartime</a><S>(&self, exp: S) -> Fp <span class="where fmt-newline">where<br> S: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.AsRef.html" title="trait core::convert::AsRef">AsRef</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u64.html">u64</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">]</a>>, </span></h4></section></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Field-for-Fq" class="impl has-srclink"><a href="#impl-Field-for-Fq" class="anchor"></a><h3 class="code-header in-band">impl <a class="trait" href="trait.Field.html" title="trait halo2_proofs::arithmetic::Field">Field</a> for Fq</h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.sqrt-1" class="method trait-impl has-srclink"><a href="#method.sqrt-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.sqrt" class="fnname">sqrt</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Fq></h4></section></summary><div class="docblock"><p>Computes the square root of this element, if it exists.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.invert-1" class="method trait-impl has-srclink"><a href="#method.invert-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.invert" class="fnname">invert</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Fq></h4></section></summary><div class="docblock"><p>Computes the multiplicative inverse of this element,
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failing if the element is zero.</p>
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</div></details><section id="method.random-1" class="method trait-impl has-srclink"><a href="#method.random-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.random" class="fnname">random</a>(rng: impl <a class="trait" href="https://rust-random.github.io/rand/rand_core/trait.RngCore.html" title="trait rand_core::RngCore">RngCore</a>) -> Fq</h4></section><section id="method.zero-1" class="method trait-impl has-srclink"><a href="#method.zero-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.zero" class="fnname">zero</a>() -> Fq</h4></section><section id="method.one-1" class="method trait-impl has-srclink"><a href="#method.one-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.one" class="fnname">one</a>() -> Fq</h4></section><section id="method.double-1" class="method trait-impl has-srclink"><a href="#method.double-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.double" class="fnname">double</a>(&self) -> Fq</h4></section><section id="method.square-1" class="method trait-impl has-srclink"><a href="#method.square-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.square" class="fnname">square</a>(&self) -> Fq</h4></section><section id="method.pow_vartime-2" class="method trait-impl has-srclink"><a href="#method.pow_vartime-2" class="anchor"></a><h4 class="code-header">fn <a href="#method.pow_vartime" class="fnname">pow_vartime</a><S>(&self, exp: S) -> Fq <span class="where fmt-newline">where<br> S: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.AsRef.html" title="trait core::convert::AsRef">AsRef</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u64.html">u64</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">]</a>>, </span></h4></section></div></details><h2 id="implementors" class="small-section-header">Implementors<a href="#implementors" class="anchor"></a></h2><div class="item-list" id="implementors-list"></div><script type="text/javascript" src="../../implementors/ff/trait.Field.js" async></script></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="halo2_proofs" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.62.0-nightly (30f386087 2022-05-05)" ></div>
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